A.W. Tozer emphasizes the importance of genuine Christian experience while preaching Christ as the Savior. He shares his personal journey, highlighting how a street preacher's words led him to earnestly seek Jesus and ultimately surrender his heart to Him. Tozer affirms that Jesus continues to call us to come to Him for rest and salvation, illustrating that true transformation begins in the heart. His testimony serves as a reminder that anyone can have a personal relationship with Christ, regardless of their background.